Cofiniteness with respect to extension of Serre subcategories

2022/05/28 by Alipour, Negar, Sazeedeh, Reza
#13D45 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2205.14533

Abstract

Let R be a commutative noetherian ring, \frak a be an ideal of R, S be an arbitrary Serre subcategory of R-modules satisfying the condition C_{\frak a} and let N be the subcategory of finitely generated R-modules. In this paper, we define and study NS-\frak a-cofinite modules with respect to the extension subcategory NS as an generalization of the classical notion, namely \frak a-cofinite modules. For the lower dimensions, we show that the classical results of \frak a-cofiniteness hold for the new notion.

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